Breadcrumbs

You are here:

We consider a generalized Stokes equation with problem parameters ξ ≥ 0 (size of the reaction term)
and ν > 0 (size of the diffusion term). We apply a standard finite element method for discretization.
The main topic of the paper is a study of efficient iterative solvers for the resulting discrete saddle point
problem. We investigate a coupled multigrid method with Braess-Sarazin and Vanka type smoothers,
a preconditioned MINRES method and an inexact Uzawa method. We present a comparative study
of these methods. An important issue is the dependence of the rate of convergence of these methods
on the mesh size parameter and on the problem parameters ξ and ν. We give an overview of the main
theoretical convergence results known for these methods. For a three dimensional problem, discretized
by the Hood-Taylor P2 − P1 pair, we give results of numerical experiments. Copyright c 2006 John
Wiley & Sons, Ltd.